A Novel Higher-Order Shear and Normal Deformation Theory for Accurate Bending Analysis of Thick Beams

This paper introduces a novel higher-order shear and normal deformation theory (HOSNDT) for bending analysis of thick beams, addressing the limitations of existing beam theories and providing significantly improved accuracy in predicting stress and strain distributions. Unlike conventional approaches, the proposed HOSNDT model employs a sophisticated fifth-order polynomial function, meticulously developed and validated through MATLAB simulations. The theory is applied to simply supported beams constructed from materials with constant elasticity modulus and functionally graded materials, showcasing its versatility and robustness. Key parameters, including transverse displacement, transverse shear stress, and axial normal stress, are analyzed comprehensively, with boundary constraints free of traction ensuring the model’s broader applicability across diverse structural configurations. The inadequacies of conventional beam theories in describing the stress-strain distribution in thick beams are highlighted. The proposed four-variable model addresses these challenges effectively by incorporating both normal and transverse shear deformations, resulting in more precise and reliable predictions of beam behavior under varied loading conditions. Comprehensive experiments validate the model’s improved stability and accuracy, demonstrating its potential as a powerful tool for structural engineering applications. These findings establish a solid foundation for future research on diverse beam configurations and advanced material combinations, offering promising directions for innovation in structural engineering analysis, optimization, and design.